MathDB
Given equation regarding areas, prove triangle is isosceles

Source:

October 12, 2010
geometryincenteranalytic geometryangle bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle with interior angle bisectors AA1,BB1,CC1AA_1, BB_1, CC_1 and incenter II. If σ[IA1B]+σ[IB1C]+σ[IC1A]=12σ[ABC]\sigma[IA_1B] + \sigma[IB_1C] + \sigma[IC_1A] = \frac{1}{2}\sigma[ABC], where σ[ABC]\sigma[ABC] denotes the area of ABCABC, show that ABCABC is isosceles.
Back to ProblemsView on AoPS